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Essentials of
Investment Analysis
and
Portfolio Management
by Frank K. Reilly & Keith C. Brown
Chapter 1
The Investment Setting
2
Why Do Individuals Invest ?
By saving money (instead of
spending it), individuals tradeoff
present consumption for a larger
future consumption.
(consumption choice)
3
How Do We Measure the Rate Of
Return On An Investment ?
The pure rate of interest is the
exchange rate between future
consumption and present
consumption. Market forces
determine this rate.
4
How Do We Measure the Rate Of
Return On An Investment ?
People’s willingness to pay
the difference for borrowing
today and their desire to
receive a surplus on their
savings give rise to an
interest rate referred to as
the pure time value of money.
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How Do We Measure the Rate Of
Return On An Investment ?
If the future payment will be
diminished in value because of
inflation, then the investor will
demand an interest rate higher
than the pure time value of
money to also cover the
expected inflation expense.
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If the future payment from
the investment is not
certain (uncertainty), the
investor will demand an
interest rate that exceeds
the pure time value of
money plus the inflation
rate to provide a risk
premium to cover the
investment risk.
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Defining an Investment
A current commitment of $ for a
period of time in order to derive
future payments that will
compensate for:
– the time the funds are committed
– the expected rate of inflation
– uncertainty of future flow of funds.
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• A central question in
investments:
How investors select
investments that will give
them their required rate of
return.
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Measures of return and risk
We have to know:
• Historical rate of return for an
individual investment over one
period of time
• Average historical return for
an individual investment over
a number of time periods
• Average return for a portfolio
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Measures of
Historical Rates of Return
Holding Period Return
Ending Value of Investment
HPR 
Beginning Value of Investment
$220
for example :
 1.10
$200
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Holding Period Yield
HPY = HPR - 1
Prior example:
1.10 - 1 = 0.10 = 10%
12
Annual Holding Period Return
•Annual HPR = HPR
1/n
n = number of years the investment is
held
Annual Holding Period Yield
•Annual HPY = Annual HPR 1
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For instance (page 7)
• A two-year HPR=$350/$250=1.4
• Annual HPR=1.4 (1/2) =1.1832
• Annual HPY=1.1832-1=18.32% (Annual
HPY is thus assumed constant for each
year)
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• However, if the prior
example is for a time period
of 6 months, what is the
annual HPR?
(Try it out!)
15
Computing mean historical
returns
Arithmetic Mean (AM) for an
investment over a number of time
periods
HPY

AM 
n
where:
 HPY
 the sum of annual
holding perio d yields
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Geometric Mean (GM)
GM  π HPR  n  1
1
where:
π  the product operator
π HPR  HPR1  HPR2    HPRn 
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HPY for a portfolio
The mean historical rate of
return for a portfolio is
measured as the weighted
average of the HPYs for the
individual investments.
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• You can also consider the
mean historical rate of return
of a portfolio as the overall
change in value of the original
portfolio.
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Computation example of HPY
for a portfolio
Exhibit 1.1
Stock
A
B
C
Total
#
Shares
100,000
200,000
500,000
HPY =
Begin
Price
$ 10
$ 20
$ 30
Beginning
Mkt. Value
$ 1,000,000
$ 4,000,000
$ 15,000,000
$ 20,000,000
Ending
Ending
Price
Mkt. Value
$ 12
$ 1,200,000
$ 21
$ 4,200,000
$ 33
$ 16,500,000
$ 21,900,000
HPR =
$ 21,900,000
$ 20,000,000
=
1.095
1.095
-1
=
0.095
=
9.5%
Market
HPR HPY
Wt.
1.20 20%
0.05
1.05
5%
0.20
1.10 10%
0.75
Wtd.
HPY
0.010
0.010
0.075
0.095
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Expected Rates of Return
• Risk: uncertainty that an
investment will earn its expected
rate of return (historical
return=realized return)
• Point estimate: He/she expects to
earns 10% over a year.
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Computing expected return
Expected Return  E(Ri )
n
  (Probabili ty of Return)  (Possible Return)
i 1
 P1 R1  P2 R2  ...  Pn Rn
n
  Pi Ri
i 1
See the detailed computation shown on page 12.
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Probability Distributions
Risk-free Investment (perfect certainty)
1.00
0.80
0.60
0.40
0.20
0.00
-5%
0%
5%
10%
15%
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Probability Distributions
Risky investment with 3 possible rates of returns
1.00
0.80
0.60
0.40
0.20
0.00
-30%
-20%
-10%
0%
10%
20%
30%
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Probability Distributions
Risky investment with 10 possible rates of return
1.00
0.80
0.60
0.40
0.20
0.00
-40%
-30%
-20%
-10%
0%
10%
20%
30%
40%
50%
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Risk Aversion
Most investors will choose the least
risky alternative, all else being equal
and that they will not accept
additional risk unless they are
compensated in the form of higher
return.
Compare the perfect certainty case and the risky
investment case on page 12.
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Measuring the risk of
expected rates of return
Variance
n
  (Probabilit y)  (Possible Return - Expected Return) 2
i 1
n
  Pi  [ Ri  E ( Ri )]2
i 1
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Measuring the risk of
expected rates of return
Standard deviation is the square
root of the variance =
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Measuring the risk of
expected rates of return
Coefficient of variation (CV) a
measure of relative variability
that indicates risk per unit of
return. C.V.  σ i
E(R)
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Measuring the risk of
historical rates of return
1.10
n
σ   [HPYi  E(HPY)] /n
2
2
i 1
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Determinants of
required rates of return
• Time value of money
• Expected rate of inflation
• Risk involved
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• Required rate of return: the minimum
rate of return to compensate for
deferring consumption.
Find out the characteristics of the yield data in
Exhibit 1.5:
1. Cross-section
2. Time series
3. Yield spread
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The components that determine the
required rate of return
The Real Risk Free Rate (RRFR)
•
•
•
•
•
The basic interest rate
Assumes no inflation
Assumes no uncertainty about future cash flows.
Pure time value of money
Influenced by time preference for consumption of
income (subjective) and investment opportunities in
the economy (objective)
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Factors for nominal risk-free rate (NRFR)
1+Nominal RFR
=(1+Real RFR)(1+Rate of Inflation)
 (1  Nominal RFR) 
1
Real RFR = 

 (1  Rate of Inflation) 
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• Real RFR is quite stable over time.
• Nominal RFR can be affected by
– The relative ease or tightness in the
capital markets
– Expected rate of inflation
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Risk Premium
• We demand a higher return on an
investment if we perceive that its
uncertainty about expected return is
higher.
• The increase in required return over
the NRFR is called risk premium.
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The major sources of uncertainty
(fundamental risk)
•
•
•
•
•
Business risk
Financial risk
Liquidity risk
Exchange rate risk
Country risk
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Business Risk
• Uncertainty of income flows
• Sales or earnings volatility
leverage affects the level of
business risk.
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Financial Risk (financial leverage)
• Uncertainty caused by the use of debt
financing.
• Borrowing requires fixed payments
which must be paid ahead of payments
to stockholders.
• The use of debt increases uncertainty of
stockholder income and causes an
increase in the stock’s risk premium.
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Liquidity Risk
• Uncertainty is introduced by the
secondary market for an investment.
– How long will it take to convert an
investment into cash?
– How certain is the price that will be
received?
• US T-bills has almost no liquidity risk.
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Exchange Rate Risk
Uncertainty of return is introduced by
acquiring securities denominated in a
foreign currency.
• To measure exchange rate risk:
Use absolute variability of exchange rate
relative to a composite exchange rate.
•
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Country Risk
• Political risk is the uncertainty of
returns caused by the possibility of a
major change in the political or
economic environment in a country.
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Risk Premium
Basically,
Risk premium= f (Business Risk,
Financial Risk, Liquidity Risk,
Exchange Rate Risk, Country
Risk)
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Pages 22-27
•Risk premium and portfolio theory
•Fundamental risk vs systematic risk
•Relationship between risk and
return
→Will be further discussed in the
later chapters
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Exercises
• Do Problem 1, 5, 7, 9.
• Read Appendix of Chapter 1 (This is
extra reading. Of course you need to
read the contents of all chapters we
discuss!)
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